Error evaluation of Judd-Ofelt spectroscopic analysis.

Judd-Ofelt (J-O) spectroscopic knowledge of a rare-earth-doped luminescent material is crucial to its application. Although a large number of papers with regard to the J-O study of various rare-earth-doped luminescent materials have been reported each year, few papers presented the errors of the J-O intensity parameters Ω (i = 2, 4, 6) and radiative probabilities evaluated from them. Present study focuses on the error evaluation of the J-O parameters and radiative probabilities. An error theory is established for the J-O analysis and radiative probability. Two error analysis methods based on root mean square of the difference either between measured and calculated oscillator strengths (δf) or between measured and calculated line strengths (δS) are studied. Explicit error expressions are presented for the J-O parameters and radiative probability. The validity of the theory is verified by applying it to widely studied Er, Tm, Ho and Nd ions that are doped into four single-crystals (LiNbO, SrGdGaO, LiYF and YVO) and a glass. The two methods are identical in nature and give similar results of errors of Ω.